PURPOSE: A dimethyl ether common rail fuel supply device and a method thereof are provided to improve durability of an engine by increasing flow rate of fuel in order to lower average temperature of the fuel and by maintaining a fuel state as liquid. CONSTITUTION: A dimethyl ether common rail fuel supply device comprises a fuel tank(10), a lower pressure pump(20), a cooling device(30), a fuel pump(40), a common rail(50), an injector(60), and a fuel amount control valve(41). The fuel tank stores a dimethyl ether fuel, and the lower pressure pump transfers the dimethyl ether fuel to a fuel supply line(L). The cooling device firstly lowers temperature of the dimethyl ether fuel. The fuel tank generates high pressure and transfers the dimethyl ether fuel to the common rail. The common rail maintains the pressure generated by the fuel pump and transfers the pressure to each injector. The injector comprises a bypass line(B) in an upper stream. The fuel amount control valve is installed in the bypass line and directly controls the fuel from the fuel pump along the bypass line with the injector.